Navier-Stokes equations with absorption under slip boundary conditions: existence, uniqueness and extinction in time

摘要

The Navier-Stokes equations modified with absorption terms under slip boundary conditions are investigated in a cylinder Ω× (0, T) C R~N × R~+. On the boundary partial derivΩ, we assume there is no-penetration of fluid flow and the slip is considered with or without friction. We present several results concerning a localization in time effect for different absorption terms. This property is established by using a suitable energy method and is independent if the slip on boundary occurs with friction or not. We prove, also, existence and uniqueness results for the related mathematical model.